Abstract
The purpose of this paper is to investigate the asymptotic stability of the zero solution of x (4)+ϕ( x ̈ ) x ⃛ +f(x, x ̇ ) x ̈ +g( x ̇ )+h(x)=0 with p≡0 and the boundedness of all solutions of x (4)+ϕ( x ̈ ) x ⃛ +f(x, x ̇ ) x ̈ +g( x ̇ )+h(x)=0 with p≠0. The results obtained here revise the results in [Demonstratio Math. 31(1) (1998) 87] and improve and includes some results in the relevant literature [J. Math. Anal. Appl. 5 (1962) 136; J. London Math. Soc. 37 (1962) 28; J. London Math. Soc. 42 (1967) 51; SIAM. J. Math. Anal. 1 (1970) 27; Int. J. Control. 69(2) (1998) 353].
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